Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

Most scientific models are not physical objects, and this raises important questions. What sort of entity are models, what is truth in a model, and how do we learn about models? In this paper I argue that models share important aspects in common with literary fiction, and that therefore theories of fiction can be brought to bear on these questions. In particular, I argue that the pretence theory as developed by Walton (1990, Mimesis as make-believe: on the foundations of the (...) representational arts. Harvard University Press, Cambridge/MA) has the resources to answer these questions. I introduce this account, outline the answers that it offers, and develop a general picture of scientific modelling based on it. (shrink)

Summary of the talk given to the 22nd Conference on the History of Logic, Cracow (Poland), July 5–9, 1976.

On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined whether (...) it will land heads or tails.2 On the other hand, we commonly assign probabilities to the different outcomes a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics (which is still an important part of modern physics) assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved? (shrink)

The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error (SME). A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account (...) by substituting probabilistic predictions for point predictions. This route is foreclosed in the case of SME, which puts us in a worse epistemic situation than SDIC. (shrink)

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

A gas prepared in a non-equilibrium state will approach equilibrium and stay there. An influential contemporary approach to Statistical Mechanics explains this behaviour in terms of typicality. However, this explanation has been criticised as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases which are epsilon-ergodic are typical with respect to the Whitney topology. Because equilibrium states are typical, (...) we argue that there follows the desired conclusion that typical initial conditions approach equilibrium and stay there. (shrink)

Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental practice. The root cause of the difficulties is the status of the Averaging Principle, the proposition that what we observe in an experiment is the ensemble average of a phase function. We review different stances toward this principle, and eventually present a coherent (...) interpretation of GSM that provides an account of the status and scope of the principle. (shrink)

Machine ethics and robot rights are quickly becoming hot topics in artificial intelligence and robotics communities. We will argue that attempts to attribute moral agency and assign rights to all intelligent machines are misguided, whether applied to infrahuman or superhuman AIs, as are proposals to limit the negative effects of AIs by constraining their behavior. As an alternative, we propose a new science of safety engineering for intelligent artificial agents based on maximizing for what humans value. In particular, we challenge (...) the scientific community to develop intelligent systems that have human-friendly values that they provably retain, even under recursive self-improvement. (shrink)

At first blush, the idea that fictions play a role in science seems to be off the mark. Realists and antirealists alike believe that science instructs us about how the world is. Fiction not only seems to play no role in such an endeavour; it seems to detract from it. The aims of science and fiction seem to be diametrically opposed and a view amalgamating the two rightly seems to be the cause of discomfort and concern.

The views on in vitro fertilization within Russian Orthodox Christian society are diverse. One reason for that variation is the ambiguity found in “The Basis of the Social Concept,” the document issued in 2000 by the Russian Orthodox Church and considered to be the primary guidelines for determining the Church’s stance on bioethics. This essay explores how the treatment of infertility reconciles with the Orthodox Christian faith and what methods of medical assistance for infertility may be appropriate for Orthodox Christians. (...) The focus here is on IVF because it is among the most widely used methods to overcome childlessness, and the permissibility of IVF is the object of disagreement among Orthodox. The article defines criteria that can help to discern what is absolutely wrong and must be avoided from what only falls short of the mark, but not very far, for Orthodox Christians. If treatment of the underlying causes of infertility has failed or promises no hope and a husband and a wife do not feel able to carry the Cross of infertility, then from pastoral dispensation they might be blessed to use ethically acceptable variants of IVF. IVF has many variants that are different in their spiritual influence on a person. Orthodox Christians pursuing IVF should seek spiritual guidance and a blessing to pursue IVF. They must not form more embryos than will be transferred in the same cycle. Freezing, discarding, or reduction of embryos is forbidden. Infertile couples ought to use only their reproductive cells. The use of donor gametes is unacceptable. Any embryo formed ought to be transferred into the wife’s womb, and the use of surrogates is impermissible. Only a husband and wife who are able to maintain their marital union and where the wife is still of childbearing age should be blessed to use IVF. (shrink)

Consider a gas that is adiabatically isolated from its environment and confined to the left half of a container. Then remove the wall separating the two parts. The gas will immediately start spreading and soon be evenly distributed over the entire available space. The gas has approached equilibrium. Thermodynamics (TD) characterizes this process in terms of an increase of thermodynamic entropy, which attains its maximum value at equilibrium. The second law of thermodynamics captures the irreversibility of this process by positing (...) that in an isolated system such as the gas entropy cannot decrease. The aim of statistical mechanics (SM) is to explain the behavior of the gas and, in particular, its conformity with the second law in terms of the dynamical laws governing the individual molecules of which the gas is made up. In what follows these laws are assumed to be the ones of Hamiltonian classical mechanics. We should not, however, ask for an explanation of the second law literally construed. This law is a universal law and as such cannot be explained by a statistical theory. But this is not a problem because we.. (shrink)

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of Shannon's (...) communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)

A weakly o-minimal structure image expanding an ordered group is called nonvaluational iff for every cut left angle bracketC,Dright-pointing angle bracket of definable in image, we have that inf{y−x:xset membership, variantC,yset membership, variantD}=0. The study of nonvaluational weakly o-minimal expansions of real closed fields carried out in [D. Macpherson, D. Marker, C. Steinhorn,Weakly o-minimal structures and real closed fields, Trans. Amer. Math. Soc. 352 5435–5483. MR1781273 (2001i:03079] suggests that this class is very close to the class of o-minimal expansions of (...) real closed fields. Here we further develop this analogy. We establish an o-minimal style cell decomposition for weakly o-minimal non-valuational expansions of ordered groups. For structures enjoying such a strong cell decomposition we construct a canonical o-minimal extension. Finally, we make attempts towards generalizing the o-minimal Euler characteristic to the class of sets definable in weakly o-minimal structures with the strong cell decomposition property. (shrink)

Scientific discourse is rife with passages that appear to be ordinary descriptions of systems of interest in a particular discipline. Equally, the pages of textbooks and journals are filled with discussions of the properties and the behavior of those systems. Students of mechanics investigate at length the dynamical properties of a system consisting of two or three spinning spheres with homogenous mass distributions gravitationally interacting only with each other. Population biologists study the evolution of one species procreating at a constant (...) rate in an isolated ecosystem. And when studying the exchange of goods, economists consider a situation in which there are only two goods, two perfectly rational agents, no restrictions on available information, no transaction costs, no money, and dealings are done immediately. Their surface structure notwithstanding, no competent scientist would mistake descriptions of such systems as descriptions of an actual system: we know very well that there are no such systems. These descriptions are descriptions of a model-system, and scientists use model-systems to represent parts or aspects of the world they are interested in. Following common practice, I refer to those parts or aspects as target-systems. What are we to make of this? Is discourse about such models merely a picturesque and ultimately dispensable façon de parler? This was the view of some early twentieth century philosophers. Duhem (1906) famously guarded against confusing model building with scientific theorizing and argued that model building has no real place in science, beyond a minor heuristic role. The aim of science was, instead, to construct theories, with theories understood as classificatory or representative structures systematically presented and formulated in precise symbolic.. (shrink)

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [2] for sets and functions definable in models of weakly o-minimal theories. We pay special attention to large subsets (...) of Cartesian products of definable sets, showing that if X, Y and S are non-empty definable sets and S is a large subset of X × Y, then for a large set of tuples $\langle \overline{a}_{1},\ldots,\overline{a}_{2^{k}}\rangle \in X^{2^{k}}$ , where k = dim(Y), the union of fibers $S_{\overline{a}_{1}}\cup \cdots \cup S_{\overline{a}_{2^{k}}}$ is large in Y. Finally, given a weakly o-minimal structure ������, we find various conditions equivalent to the fact that the topological dimension in ������ enjoys the addition property. (shrink)

This paper attempts to formalize and to address the ‘leakproofing’ of the Singularity problem presented by David Chalmers. The paper begins with the definition of the Artificial Intelligence Confinement Problem. After analysis of existing solutions and their shortcomings, a protocol is proposed aimed at making a more secure confinement environment which might delay potential negative effect from the technological singularity while allowing humanity to benefit from the superintelligence.

In this paper the completeness theorems for the finite-valued ukasiewicz logics are proved with the use of the Lindenbaum algebra.

A model M of PA has the omega-property if it has a subset of order type omega that is coded in an elementary end extension of M. All countable recursively saturated models have the omega-property, but there are also models with the omega-property that are not recursively saturated. The papers is devoted to the study of structural properties of such models.

We develop multi-conclusion nested sequent calculi for the fifteen logics of the intuitionistic modal cube between IK and IS5. The proof of cut-free completeness for all logics is provided both syntactically via a Maehara-style translation and semantically by constructing an infinite birelational countermodel from a failed proof search. Interestingly, the Maehara-style translation for proving soundness syntactically fails due to the hierarchical structure of nested sequents. Consequently, we only provide the semantic proof of soundness. The countermodel construction used to prove completeness (...) required a completely novel approach to deal with two independent sources of non-termination in the proof search present in the case of transitive and Euclidean logics. (shrink)

Im Blickpunkt dieses Bandes steht das Wechselverhältnis zweier prägender Traditionen moderner deutschsprachiger Philosophie: der Kritischen Theorie und der Philosophischen Anthropologie. Über das gesamte 20. Jahrhundert hinweg blieb der Austausch zwischen diesen Ansätzen, wo er überhaupt zu Stande kam, von Vorbehalten geprägt. Gegenwärtig allerdings lässt sich, jenseits überkommener schulpolitischer Gräben, ein neuartiges Interesse beider Strömungen füreinander wahrnehmen. Die Beiträge dieses Bandes treffen sich in dem Versuch, die jeweiligen Hauptanliegen und Gegenstandsfelder der Kritischen Theorie respektive der Philosophischen Anthropologie über deren direkten Dialog (...) produktiv zu aktualisieren: Inwiefern lassen sich die genuinen Themen der einen Tradition auf Seiten der je anderen rekonstruieren? Und worin bleiben sich beide Denkweisen letztlich doch fremd? Das vorliegende Buch stellt in der Forschung den ersten systematischen Versuch dar, diese Fragen für gesellschaftstheoretische und anthropologische Problemstellungen fruchtbar zu machen. (shrink)

We prove a number of results concerning the variety of first-order theories and isomorphism types of pairs of the form $(N,M)$ , where $N$ is a countable recursively saturated model of Peano Arithmetic and $M$ is its cofinal submodel. We identify two new isomorphism invariants for such pairs. In the strongest result we obtain continuum many theories of such pairs with the fixed greatest common initial segment of $N$ and $M$ and fixed lattice of interstructures $K$ , such that $M\prec (...) K\prec N$. (shrink)

In its most common use, the term ‘model’ refers to a simplified and stylised version of the socalled target system, the part or aspect of the world that we are interested in. For instance, in order to determine the orbit of a planet moving around the sun we model the planet and the sun as perfect homogenous spheres that gravitationally interact with each other but nothing else in the universe, and then apply Newtonian mechanics to this system, which reveals that (...) the planet moves on an elliptical orbit. Views diverge about what sort of entity such a model is. Those focussing on the formal aspects of models regard them either as equations or settheoretical structures, while those opposed to such an approach take them to be descriptions or abstract (yet non-mathematical) entities. A further question concerns the relation of models and theories. In some cases models can be derived from theory simply by specifying the relevant determinables in a theory’s general equations. But many models cannot be obtained from theory in this straightforward way, and some even involve assumptions that contradict the fundamental theory. The relation of models to their respective target systems is equally complex and fraught with controversy. Two influential proposals take the relation between a model and its target to be isomorphism or similarity, respectively. This, however, has been criticised as too restrictive as many models do not seem to fit this mould. (shrink)

Авторами розглянуто вплив провідних світових кредитних рейтингових агентств на фінансову безпеку емітентів цінних паперів. Обґрунтовано перформативний характер діяльності кредитних рейтингових агентств з позицій моделі «Les economies de la grandeur» нового соціологічного французького інституціоналізму, що дає змогу розв’язати протиріччя щодо сильної опозиції стосовно їх функціонування з одночасним збереженням діючої системи нормативного використання кредитних рейтингів.

We discuss Robinson's model theoretic proof of Tarski's theorem on undefinability of truth. We present two other “diagonal-free” proofs of Tarski's theorem, and we compare undefinability of truth to other forms of undefinability in nonstandard models of arithmetic.

By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long time, (...) the real, ideal numbers of Plato’s Ideal mathematics eliminates many mathematical problems, extends the capabilities of modelling, and improves mathematics. (shrink)

Let (M, ≤,...) denote a Boolean ordered o-minimal structure. We prove that a Boolean subalgebra of M determined by an algebraically closed subset contains no dense atoms. We show that Boolean algebras with finitely many atoms do not admit proper expansions with o-minimal theory. The proof involves decomposition of any definable set into finitely many pairwise disjoint cells, i.e., definable sets of an especially simple nature. This leads to the conclusion that Boolean ordered structures with o-minimal theories are essentially bidefinable (...) with Boolean algebras with finitely many atoms, expanded by naming constants. We also discuss the problem of existence of proper o-minimal expansions of Boolean algebras. (shrink)

In order to „open us fuller and better to Europe", we are starting with a new review FORUM PHILOSOPHICUM. FORUM will be published once a year in English, French, German, Italian, Spanish, Latin and Polish. The articles in Polish will be followed by extensive summaries in foreign languages. Since we do not renounce Polish speaking readers, the articles in foreign languages are also followed by extensive summaries in Polish.

Poniższe opracowanie obejmuje zasadniczo wiek XX. Nawiązuje jednak do pewnych dokumentów i faktów z XIX w., które miały znaczny wpływ na kształt filozofii jezuitów w XX w. Chodzi zwłaszcza o nową wersję dawnej Ratio studiorum z 1832 r. oraz o encyklikę Aeterni Patris z 1879 r. Badając dzieje filozofii jezuitów w Polsce, można wyróżnić: 1) filozofia związana z nauczaniem, głównie w Wydziale Filozoficznym Towarzystwa Jezusowego w Krakowie, oraz 2) filozofia pozaszkolna, a więc nie związana ścisłej z nauczaniem.

Le livre presente le probleme de la transcendance de Thomme d'apres les createurs de l'Ecole de Philosophie de Lublin. Cette ecole est nee a Lublin dans le milieu de l'Universite Catholique apres la deuxieme guerre mondiale. Elle est representee par des penseurs comme M. A. Krąpiec OP et le Cardinal K. Wojtyła. Ces deux philosophes ont aborde, dans leurs recherches, des problemes anthropologiques et ils ont presente une theorie interessante de l'homme. Dans leur theorie, la transcendance de l'homme est mise (...) en relief d'une fagon particuliere. C'est la dimension de I'homme qui decide de la priorite de son etre, de sa dignite et de sa valeur parmi les autres etres dans le monde. (shrink)

Józef Alojzy [Josephus Aloisius] Dmowski was one of the precursors of the nineteenth century renewal of Thomism and this was a few dozen years before the promulgation of Pope Leo XIII's encyclical, Aeterni Patris. He was one of the most famous Christian philosophers of the nineteenth century. His work was also the first extensive philosophy textbook of that time which included a l l the disciplines of the time, published by the Jesuits after the re-establishment of the Order in 1814.. (...) Until now Dmowski's philosophy has not been the subject of an extensive study. I aim to remedy this in the present article. (shrink)